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Theorem dmv 5640
Description: The domain of the universe is the universe. (Contributed by NM, 8-Aug-2003.)
Assertion
Ref Expression
dmv dom V = V

Proof of Theorem dmv
StepHypRef Expression
1 ssv 3883 . 2 dom V ⊆ V
2 dmi 5639 . . 3 dom I = V
3 ssv 3883 . . . 4 I ⊆ V
4 dmss 5622 . . . 4 ( I ⊆ V → dom I ⊆ dom V)
53, 4ax-mp 5 . . 3 dom I ⊆ dom V
62, 5eqsstr3i 3894 . 2 V ⊆ dom V
71, 6eqssi 3876 1 dom V = V
Colors of variables: wff setvar class
Syntax hints:   = wceq 1507  Vcvv 3415  wss 3831   I cid 5312  dom cdm 5408
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1758  ax-4 1772  ax-5 1869  ax-6 1928  ax-7 1965  ax-8 2052  ax-9 2059  ax-10 2079  ax-11 2093  ax-12 2106  ax-13 2301  ax-ext 2750  ax-sep 5061  ax-nul 5068  ax-pr 5187
This theorem depends on definitions:  df-bi 199  df-an 388  df-or 834  df-3an 1070  df-tru 1510  df-ex 1743  df-nf 1747  df-sb 2016  df-mo 2547  df-eu 2583  df-clab 2759  df-cleq 2771  df-clel 2846  df-nfc 2918  df-ral 3093  df-rex 3094  df-rab 3097  df-v 3417  df-dif 3834  df-un 3836  df-in 3838  df-ss 3845  df-nul 4181  df-if 4352  df-sn 4443  df-pr 4445  df-op 4449  df-br 4931  df-opab 4993  df-id 5313  df-xp 5414  df-rel 5415  df-dm 5418
This theorem is referenced by: (None)
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